(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There are two log properties that I have to prove:

1) Explain why ln(b^{1/n})=(1/n)ln(b) for b>0, set b=a^{n}

2) Explain why ln(a^{r})=rln(a) for any r in Q and a>0, ie r is rational.

2. Relevant equations

ln(a^{n})=nln(a)

3. The attempt at a solution

In a previous question I have already proved that ln(a^{n})=nln(a), where n is a natural number. What I'm unsure about, is how is this any different? For 1), I'm not sure why you set b=a^{n}? Wouldn't you get ln((a^{n})^{1/n}) = ln(a)? I'm not sure how this helps me find the solution.

Similarly for 2), I'm unsure how it is any different to proving that ln(a^{n})=nln(a).

Any help would be great!

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# Homework Help: Proof of logarithmic properties.

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